Thermodynamics of Fluids Under Flow

Entropy Principle and Recent Results in Non-Equilibrium Theories

“…The assumption of zero antisymmetric part in Equation (20) ensures the existence of a scalar potential whose derivative by ∂ k z α is the J k − Λ α Φ α k vector field (see e.g., [71]). Let us observe, that the final result of this simple derivation, the entropy production in the form of Equation (21), corresponds only to the structure of the second, thermal term in Equation (10). The first, mechanical term is different.…”

“…From here, using the definition (1) for the entropy production, one is led for the entropy production to a quadratic form which is a sum of products of fluxes times generalized thermodynamic forces, and it is required that the constitutive equations are submitted to the restriction that the entropy production is positive definite. The main differences with the entropy principle in CIT are [8][9][10]:…”

“…In extended irreversible thermodynamics (EIT), taking the fluxes as independent variables, the three questions mentioned above give the following answers [8][9][10][11][12][13]:…”

A thermodynamic model of nanofluid viscosity based on a generalized Maxwell-type constitutive equation

“…The generalization to more complicated systems as fluids mixtures [26], polymer solutions [27], suspensions [28], porous media [29] and others have been dealt with in detail in numerous publications and books. In the case of an incompressible fluid flow, the only relevant conserved variable is the specific internal energy e (per unit mass)) whereas the corresponding flux variable is the viscous pressure tensor P, it is a second order symmetric traceless tensor, in contrast with e, it is not a conserved quantity.…”

“…[27,34] In the next section, we will determine the dependence of the effective viscosity of the nanofluid with respect to the size of the nanoparticles.…”